Their show many be six seasons old, but the “Real Housewives of Atlanta” are doing just peachy.

The Jan. 5 episode of the Bravo franchise (airing Sundays at 8 p.m.) became the highest-rated in “Housewives” history with 4.5 million viewers — driving the network to its best night ever.

While other city versions may draw more headlines, cast member Kenya Moore says she and fellow Atlanta “Housewives” NeNe Leakes, Cynthia Bailey, Kandi Burruss, Phaedra Parks and Porsha Stewart offer a more palatable — and diverse — cast.

“You can’t overlook the fact that we’re an all brown-girl cast this season, but what makes our show also different from the rest is we’re funny,” Moore tells The Post. “We have all of these crazy dramas that happen and we’re exposing our lives and who we are and that is in and of itself very interesting and very compelling. But on top of all of that, we still manage to be funny and laugh at each other. It makes it easy to watch.”

Leakes agrees that the Atlanta iteration is better than other “Housewives” shows, recently telling African-American news site theGrio.com, “We’re more relatable, our issues are real, and we have the least amount of plastic surgery, while some of these other girls are nipped and tucked. We’re just very real.”

Demographics are also at play in the show’s success — according to Nielsen, 60 percent the show’s female viewers are African-American, a group traditionally under-represented on television.

“The number one thing that I would point to is literally the true multiculturalism of the cast,” says Danielle Cherry, VP, human experience strategist for media agency Starcom MediaVest Group. “When we look at ratings and we see this exceptional engagement that is happening and you see something that doesn’t look like the norm on a network, we automatically think to how much resonance this must be giving to African-American women in particular.”

Atlanta was the third “Housewives” franchise to premiere, in 2008, after Orange County and New York City, and has been the most-watched city since its second season. And unlike other editions, whose ratings have been trending down in recent seasons, Atlanta continues to grow — its current sixth season is averaging 3.5 million viewers, up from 3.1 million viewers the prior season.

That is partly attributable to a cast that’s savvy about growing their fan following, like Leakes (an original cast member) who guest-starred on the third season of “Glee” and co-starred in the short-lived NBC comedy “The New Normal” last season.

“Their cast is very well adept at making sure that they have something to say, making sure that they’re staying in the spotlight,” Cherry says.

That audience connection to the Atlanta characters has produced more spinoffs (three) than any other “Housewives” cast: “Don’t Be Tardy…” starring former cast member Kim Zolciak, “The Kandi Factory,” which followed Burruss as she helped aspiring artists jump start their careers in the music industry, and last fall’s “I Dream of NeNe: The Wedding.”

“Real Housewives of Atlanta” has also opened the door for other Bravo shows with African-American casts: “Thicker Than Water” and “Blood, Sweat & Heels,” the latter of which was Bravo’s most-watched series premiere ever on Jan. 5 with 2.5 million viewers.